The presence of a risk-free asset portion in a portfolio can insure its value with almost the same precision as purchasing put options.
The value of a diversified investment portfolio can be insured by buying a put option on the corresponding index (see in detail: Portfolio Insurance with Index Options). However, since a put option can be replicated by a suitable combination of stocks and risk-free bonds, it is also possible to provide insurance using a synthetic option.
Why create a synthetic option if you can buy a financial option?
First, because you may not be able to find an option that matches your insurance needs in terms of strike price and maturity. Second, because financial options sometimes suffer from liquidity problems, which can be avoided by using synthetic options.
Before turning to synthetic options, let us recall the replication method used in option valuation. The table below shows that an option with a strike price of $530 produces the same financial outcome in scenarios A and B as shorting the appropriate number of shares and investing the proceeds in risk-free assets. Accordingly, the price of the option must equal the value of the portfolio that replicates its payoff (see in more detail: Portfolio Replication Method).
Thus, if
PUT = T-Bill – Δ Stock
Then a hedged portfolio becomes:
Stock + PUT = Stock + (T-Bill – Δ Stock) = T-Bill + (1-Δ)*Stock
Let us look at an example. Suppose we have a stock portfolio worth $90 million and we want to insure it with a lower bound of $87 million.
The delta of a European put option is calculated using the following formulas:
From the example, we see that it is necessary to sell 32.15% of the stock value and invest the proceeds in a risk-free asset with a corresponding maturity.
Important notes:
The method of hedging with a synthetic option requires regular rebalancing. If the price moves downward, the weight of the risk-free asset in the portfolio increases, and vice versa.
In practice, a synthetic option will replicate a financial option exactly only if rebalancing between stocks and risk-free assets is carried out continuously (since changes in the stock price alter the option’s delta). Therefore, the more frequently rebalancing occurs, the closer this hedging method comes to the protection provided by a financial option.
Alternatively, the problem can be approached from the opposite direction: one may choose not to rebalance the portfolio, but instead observe what strike price of a corresponding financial option matches the existing portfolio allocation—that is, where the insured boundary lies.
Finally, it is important to note that in the case of a financial option, the option premium is paid upfront. In contrast, with a synthetic option there is no such explicit payment, but the cost is still present in the form of foregone expected returns, resulting from the reduced share of stocks in the portfolio.
Adapted from: Options, Futures & Other Derivatives, John C. Hull